Affiliations: [a] College of Mathematics, Changchun Normal University, Changchun, 130032, P.R. China. E-mail: liangsihua@126.com | [b] School of Mathematics and Statistics, Northeast Petroleum University, Daqing, 163318, P.R. China | [c] Department of Mathematics, Heilongjiang Institute of Technology, Harbin, 150050, P.R. China. E-mail: zhangbinlin2012@163.com
Abstract: In this paper, we study the following Kirchhoff type problems involving fractional p-Laplacian and critical exponents:
M([u]s,pp)(−Δ)psu=λ|u|ps∗−2u+b(x)|u|p−2u+f(x,u),in Ω,u=0in RN∖Ω,
where Ω is a bounded domain in RN (N⩾3) with Lipshcitz boundary, 1<p<N/s with s∈(0,1), ps∗=Np/(N−ps) is the fractional critical Sobolev exponent, λ is a positive parameter, M:[0,+∞)→R+ and f:Ω‾×R→R are continuous functions, b:Ω→R is a sign-changing function. By using the fractional version of concentration compactness principle together with mountain pass theorem, we obtained the multiplicity of solutions for the above problem.
